KöMaL 2006 K103

Andrew, Bill, Charlie and Dennis are playing cards. In each game, only three of the four boys are playing. They get points from one another, depending on the outcome of the game: either one player gets points from the other two or two players get points from the third one. (If there are two losers or two winners then they do not necessarily lose or gain the same number of points.) At the beginning, everyone had 100 points. The boys have played four games, each time leaving out a different person. The points that each participant had during the card play are tabulated on the diagram. Which player was left out from the respective games? Andrew Bill Charlie Dennis 100 100 100 100 110 110 90 80 125 105 80 110 85 85 100 130